WASHINGTON — Hundreds of leading business groups and GOP donors called for action on immigration legislation Tuesday, seeking to increase pressure on the House GOP as lawmakers prepare to leave Washington for a five-week summer recess.

Two letters were released separately, one signed by more than 400 leading businesses, chambers of commerce and others, and the second by around 100 GOP donors, including boldface names such as former Vice President Dan Quayle and GOP strategist Karl Rove.

Both sought to frame the immigration debate partly in economic terms that could sway majority House Republicans, who are debating how to move forward with immigration legislation after the Senate passed a comprehensive bill in June with visa reforms, border security and eventual citizenship for the 11 million immigrants already in the country illegally.

No action is expected in the House until fall, at which point Republicans may advance a piecemeal series of single-issue bills beginning with border security. The potential for the House to reach any agreement with the Senate on a final package that could reach President Barack Obama’s desk is very much in doubt.

Signers of the business letter include a range of business interests, from AT&T and IBM to the American Meat Institute, the Indiana Farm Bureau and the U.S. Chamber of Commerce.

The letter does not set out specific policies the groups are seeking but argues that the existing immigration system is “completely incapable” of responding to the national economy or global competition and says that “failure to act is not an option.”

The donor letter makes a political case in addition to an economic one, arguing that blocking action would “risk a long-lasting perception that Republicans would rather see nothing done than pass needed reform.” The letter calls for a “path to legal status” for immigrants here illegally, stopping short of calling for citizenship.

One signer of the letter, Spencer Zwick, former national finance chairman for Republican presidential nominee Mitt Romney, said that broader language was used to draw as much donor support as possible.

“I think what you want to do with a letter like that is be careful not to let one line destroy the letter,” Zwick said. “I believe if we come up with a pathway to good legal immigration, part of that does mean citizenship, but let’s take things one step at a time.”

Another signer, Carlos Gutierrez, former commerce secretary and a leader of the group Republicans for Immigration Reform, said that he’s seen some “donor fatigue” as his group tries to raise money to fight for overhauling immigration but that it would aim to spend enough to sway 12 to 15 congressional districts.

“I don’t think we’re going to be doing national TV campaigns, which can be so expensive, but we’re going to be able to make a difference in local districts where it counts,” Gutierrez said.